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On metrics defined by
modules
James Allister Jenkins |
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Vol. 167 (1995), No. 2, 289–292
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Abstract |
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Jacqueline Ferrand gave a very general definition of a conformal invariant λG(x,y) for a domain G by the use of modules of curve families and showed that, in dimension n, λG(x,y)−1∕n is a metric. The question as to whether λG(x,y)−1∕(n−1) is itself a metric was raised by Vuorinen and studied by him and Jacqueline Ferrand. In particular he asked whether this held for n = 2 and G the punctured plane. In this paper it is shown that the answer is affirmative for any domain of finite connectivity on the sphere. |
Mathematical Subject Classification 2000
Primary: 30C65
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Milestones
Received: 21 July 1992
Published: 1 February 1995
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Authors |
| James Allister Jenkins | |
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